The principal objective of this project is to investigate the gravitational lensing by asymptotically flat black holes in the framework of Horndeski theory in weak field limits. To achieve this objective, we utilize the Gauss–Bonnet theorem to the optical geometry of asymptotically flat black holes and apply the Gibbons–Werner technique to achieve the deflection angle of photons in weak field limits. Subsequently, we manifest the influence of plasma medium on deflection of photons by asymptotically flat black holes in the context of Horndeski theory. We also examine the graphical impact of deflection angle on asymptotically flat black holes in the background of Horndeski theory in plasma medium as well as non-plasma medium.

中文翻译：

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使用 Gauss-Bonnet 定理的 Horndeski 理论中渐近平坦黑洞的弱偏转角

该项目的主要目标是在弱场限制下，在 Horndeski 理论框架内研究渐近平坦黑洞的引力透镜效应。为了实现这一目标，我们将 Gauss-Bonnet 定理应用于渐近平坦黑洞的光学几何，并应用 Gibbons-Werner 技术来实现弱场极限中光子的偏转角。随后，我们在 Horndeski 理论的背景下，通过渐近平坦的黑洞证明了等离子体介质对光子偏转的影响。我们还研究了在等离子介质和非等离子介质中以 Horndeski 理论为背景的偏转角对渐近平坦黑洞的图形影响。